Ukrainian Mathematical Journal

, Volume 68, Issue 12, pp 1849–1859 | Cite as

On Generalized Statistical and Ideal Convergence of Metric-Valued Sequences

  • P. Das
  • E. Savas

We consider the notion of generalized density, namely, the natural density of weight g recently introduced in [M. Balcerzak, P. Das, M. Filipczak, and J. Swaczyna, Acta Math. Hung., 147, No. 1, 97–115 (2015)] and primarily study some sufficient and almost converse necessary conditions for the generalized statistically convergent sequence under which the subsequence is also generalized statistically convergent. Some results are also obtained in a more general form by using the notion of ideals. The entire investigation is performed in the setting of general metric spaces extending the recent results of M. Kücükaslan, U. Deger, and O. Dovgoshey, [Ukr. Math. J., 66, No. 5, 712–720 (2014)].


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • P. Das
    • 1
  • E. Savas
    • 2
  1. 1.Jadavpur UniversityWest BengalIndia
  2. 2.Istanbul Commerce UniversityIstanbulTurkey

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